The period conjecture of Grothendieck predicts the relations between the period numbers of mixed motives. In joint work with Wüstholz we have established Kontsevich's formulation of the conjecture (concentrating on linear rather than algebraic relations) for 1-motives. As a consequence this gives a sharp criterion for transcendence of periods of curves. The plan of this talk is to explain this result as well as the framework of conjectures behind it.
